


Applied Magical Mechanics

by NarcolepticEngineer



Category: Harry Potter - J. K. Rowling
Genre: Calculations, Dynamics, Engineering, Fake Science, Magic, Mechanical engineering, Mechanics, Nonfiction, Textbook Fic, statics
Language: English
Status: In-Progress
Published: 2020-08-02
Updated: 2020-08-22
Packaged: 2021-03-06 07:20:33
Rating: General Audiences
Warnings: No Archive Warnings Apply
Chapters: 3
Words: 2,080
Publisher: archiveofourown.org
Story URL: https://archiveofourown.org/works/25659616
Author URL: https://archiveofourown.org/users/NarcolepticEngineer/pseuds/NarcolepticEngineer
Summary: I have recently started writing a Harry Potter-verse textbook-fic. I'm focusing on magical engineering and physics. I'm actually pulling out my engineering textbooks on applied mechanics, statics, fluid dynamics, and machine design. It's not going to be a university-grade textbook, but I'm aiming for a basic Intro to Magical Mechanical Engineering 101 kind of thing.
Comments: 11
Kudos: 20





	1. Preface, Table of Contents

**Author's Note:**

> Table of contents listed here are currently only placeholders. I am planning to add/subtract/change, but the actual contents and how long this will end up are still to be determined!
> 
> Chapter 1 is also here, but the terminology list is ongoing... likely to be added to every consecutive chapter as I make up more terminology.
> 
> It's weird, it's unusual, but this is actually really exciting for me. And I know myself well enough that if I don't post my WIP somewhere, it shrivels up and dies.
> 
> Let me know what you think!

**Applied Magical Mechanics**

FIRST EDITION

Hyperion Somnus

Preface

Applied Magical Mechanics broadly covers the study of magic for functional utilization. Magical mechanics is more than just the teaching of mechanical principles imbued with magic; the subject teaches how magic is an important and integral part of the scientific process. It is an important methodology in developing methods of stripping problems down to essentials and solving them in a logical, organized manner. This method of working minimally incorporates, and can be additionally applied, to many other areas: including runes, warding, charms, and enchanting.

This book therefore shows a consistent pattern of creative problem solving. The physics principles are presented in small elementary steps, the arithmancy is kept at a reasonable level, and the problems are as practical as possible without becoming too involved with many extraneous details.

This text is not meant to be a comprehensive guide to magical mechanics, it is meant to be an overview or a handbook for quick reference.

Table of Contents

PART ONE: STATICS

  1. Introduction 
    1. What and Why of Applied Magical Mechanics
    2. Basic Terms and Examples
  2. Forces, Vectors, and Resultants 
    1. Vectors
    2. Resultants
  3. Moments and Enchantments 
    1. Moment of a Force
    2. Galimatic Moments
  4. Magic assisted Equilibrium 
    1. Free-Body Diagrams
    2. Multiplanar Force Systems
  5. Structures and Members 
    1. Methods of Joining
    2. Method of Sections
    3. Method of Members
  6. Plane Creation and Orientation 
    1. Three-Dimensional Equilibrium
    2. Galimatic Equilibrium
    3. Unique Planar Orientation
  7. Levitational Equilibrium 
    1. Centroids of Composite Areas
    2. Center of Gravity
  8. Runic Binding 
    1. Runic Joinery
    2. Continuous Structural Wards



PART 2: DYNAMICS

  1. Multilinear and Angular Motion
  2. Galimatic Acceleration
  3. Planar Motion
  4. Charmed Kinetic Inertia
  5. Energy Efficiency
  6. Galimancy and Power
  7. Impulse and Momentum



**Notes for the Chapter:**

> Edited this to just be Preface and Table of Contents. Chapter 1 will be in the next chapter.


	2. Chapter 1: Introduction

**Summary for the Chapter:**

> 1\. Introduction  
> 1.1. What and Why of Applied Magical Mechanics  
> 1.2. Basic Terms and Examples

1\. INTRODUCTION

1.1 WHAT AND WHY OF APPLIED MAGICAL MECHANICS

Applied magical mechanics is a branch of the meta-physical sciences and the practical application of Galimatic physics. Natural mechanics would simply describe the response of bodies (solids and fluids) or systems of bodies to external behavior of a body. However, applied magical mechanics bridges the gap between magical theory and its application to the manipulation of physical bodies. It is co-dependent on many fields of magic, especially enchanting, charms and runes; in this context, it is commonly referred to as magical mechanics. Much of modern applied or magical mechanics is based on Galileo Galilei’s work in physics; who is to this day considered the “warlock of applied astrology” and “warlock of the scientific method.” Later, his works were expanded on by Sir Isaac Newton's laws of motion. The modern practice of their application can be traced to Stephen Timoshenko (non-magical), who is said to be the father of modern engineering mechanics.

Within the meta-physical sciences, applied magical mechanics is useful in formulating new ideas and theories and developing experimental and structural tools.

1.2 UNITS AND BASIC TERMS

**CORE COEFFICIENTS**

(Abbreviation: cc, symbol: Ჵ)

This symbol appears in many arithmantic formulas and describes the capacity of the witch or wizard to be able to affect magic unto their environment. This Core Coefficient will be a value on a scale of 0 to 1.

Typically, non-magical humans register at zero or just above, and squibs less than 0.1. The high end of the scale, 1, has not been proven to be physically possible. The highest recorded cc was from Sir Isaac Newton, famous alchemist and credited with first creation of a philosopher’s stone. His score was 0.92. Albus Dumbledore is recorded at 0.71.

To determine one’s cc, witch or wizard must hold a _Lumos Iota_ for as long as possible. The _Lumos Iota_ precisely uses 2.5₰ of energy every minute. A squib or muggle can be given a minimumall, which a small glass sphere that changes color, using precisely 0.1₰ of energy every minute.

Ჵ = ₰ tm/2000

Using the formula above, Sir Isaac Newton held a Lumos Iota for approximately 736 minutes (12 hours, 16 minutes). And Albus Dumbledore held his for 568 minutes (9 hours, 28 minutes). A perfect score would be 800 minutes.

**IOTA**

(unit: io, symbol: ₰)

The Iota is a unit of magic; it is defined as the amount of magic required to raise the temperature of ten pounds of water by 10 degrees Fahrenheit. Magic is now known to be the equivalent of energy, and therefore heat.

The Mundane world uses similar units for measuring units of heat in BTUs (British Thermal Units) but offset by 2 orders of magnitude. If one wished to perform a conversion, an iota divided by 100 equals a BTU.

**GALIMATIC**

Throughout this text, magically influenced events will be often termed “ _Galimatic_ ” events.

Galimancy is the study of the physical properties of magic, credit to the great wizard Galileo Galilei who pioneered modern astrology and meta-physics. His ideas were so revolutionary that even the mundane world had benefited from his works.

Ex. When magic is utilized, for example in a feather-weight charm, we reduce the normal force by 0.5Ჵ for every Iota of magical power. Therefore, we also are reducing the friction; hence the resultant Galimatic friction is also 50% of natural.

**UNITS**

The Imperial System of Units is used predominately throughout the magical world. The system was first defined in the Magical British Empire, for the Weights, Measures, and Magicks Act of 1824.

Worldwide, it was initially popularized throughout the colonies, and since then has become the standard for all arithmantic computations for magical purposes.

**MASS**

Mass is expressed with the slug (slug). The slug is a mass that accelerates by 1 ft/s2 when a force of one pound (lb) is exerted on it.

**LENGTH**

A base length of 1 foot (ft) is used. The popular multiples are the yard (yd) equaling 3ft, and the mile (mi), equaling 5280 ft. The inch (in) equaling 1/12 ft, is used for calculations to avoid unwieldy numbers and for convenience in many cases.

**TIME**

The basic unit of time is 1 second (s). Because of universal acceptance, other permitted units are minute (min), hour (h), and day (d).

**AREA**

Area can be defined as the space occupied by a flat shape or the surface of an object. It is often measured in in2, ft2, and yd2.

**VOLUME**

Volume is the quantity of three-dimensional space enclosed by a closed surface. It is often measured in in3, ft3, and yd3.

**FORCE**

A force is any interaction that, when unopposed, will change the motion of an object. Forces have both magnitude and direction, making them vector quantities. It is most often measured in pounds (lbs).

**ANGLE**

In a full circle there are 360 degrees (°). Each degree is split up into 60 minutes (‘), each part being 1/60 of a degree. Each minute is split up into 60 seconds(“), each part being 1/60 of a minute. Notation written as: 42°23’11” for example.

**PRESSURE**

Pressure is force per unit area. Units of psi (lbs/in2) are commonly used.

**STRESS**

Stress is an internal load per unit area. It is expressed similarly to pressure, units of psi (lbs/in2) are commonly used.

**STRAIN**

Strain is a measure of length per length. Strain is primarily expressed with in./in.

**MAGIC**

Magic is the practical application of the energy residing in the core of a witch or wizard in order to affect change. Magic is quantified in iotas (₰).

**WORK**

Work is magic, and can be expressed using the iota (₰). Commonly, work is equal to force times distance, so it could be expressed as a ft-lb, however the iota is the preferred unit.

1₰ = (ft-lb)/7.78

**POWER**

Power is the rate of doing work. The horsepower (hp) is the unit used for power.

Power = work/time

1hp = 71₰/s

**MOMENT**

Moment is equal to a force times a perpendicular distance. Essentially a moment is a force times a distance, so units are expressed as ₰m to make distinction from work units.

**VELOCITY**

Velocity is a rate of change of displacement with respect to time. The units most often used are ft/s and mph.

**ANGULAR VELOCITY**

Angular velocity is the rate of change of rotational displacement with respect to time and is primarily expressed in units of degrees per second(deg/s), but revolutions per minute (rpm) is a permitted form.

**ACCELERATION**

Acceleration is the rate at which velocity changes; hence the units are ft/s2. The acceleration due to gravity is 32.2 ft/s2.

**ANGULAR ACCELERATION**

Angular Acceleration is the rate at which angular velocity changes; hence the units are deg/s2.

**DENSITY**

Because density is mass per unit volume, the units are:

lb/in3, or lb/ft3

**FREQUENCY**

One hertz is the frequency of a periodic occurrence that has a period of 1 second.

**MOMENTUM**

Momentum is mass times velocity; it is expressed in either units of slug-ft/s, or in lb-s.

**ANGULAR MOMENTUM**

Angular Momentum is the mass moment of inertia times angular velocity.

₰٠ּs2 x deg/s = ₰٠ּs


	3. Forces, Vectors, and Resultants

**Summary for the Chapter:**

> 2\. Forces, Vectors, and Resultants  
> 2.1. Vectors  
> 2.2. Resultants

2\. FORCES, VECTORS, AND RESULTANTS

As this section does not differ from non-magical engineering, this text will not go into deep details on vectors, forces, and resultants. Instead the focus will be on distinguishing properties and functional examples.

Key terms in this chapter will be emphasized in _italic_ s.

Unfortunately, due to publishing constraints, images and drawings will be explained but not shown.

2.1 VECTORS

While a force is not difficult to define as a push or a pull, while simple, there are further classifications. However, all forces do have one property in common: they can be represented by vectors.

We must first distinguish between a _vector_ quantity and a _scalar_ quantity.

  * A scalar quantity is the most familiar, indicating a size or a magnitude. For example, a board is 10 ft long, a 2-minute time interval, or a 5₰ spell.
  * Vector quantities have the additional property of direction. Some vector quantities are a force of 18 lb vertically downward, a distance of 2 miles north, a velocity of 60 mph east, an acceleration of 8 ft/sec2 A vector quantity is therefore represented by an arrow; the arrowhead indicates the direction, and the length of the arrow indicates the magnitude.



Drawing vectors to scale is only used for graphical solutions, but when drawing for analytic solutions, draw them approximately to scale for easier visualization of the problem solution. To be complete, both direction and magnitude must be labeled for each vector quantity.

2.2 RESULTANTS

Scalar quantities can be added to sum their parts for resultant quantities. But if we add vector quantities, their directions must be considered. This is known as _adding vectorially_ or _vector addition_. The answer obtained is the _resultant_ ; it is a single vector giving the result of the addition of the addition of the original two or more vectors.

“A picture is worth a thousand words,” goes the old adage; arithmantic and mechanics problems are no exception. Sketches are vitally important in many cases; calculations should be accompanied by a sketch drawn as closely to scale as easily possible with a little effort. A calculated answer can be much more effectively visually checked for obvious errors in direction or magnitude. Analytical vector addition consists of two main methods:

  1. Construction of a triangle and the use of the cosine law or other simple trigonometric functions.
  2. Addition of the components of vectors.



Without the ability to depict drawings in this publication, we will be staying mostly conceptual. If needed, refer to trigonometric texts for solving resultant vector calculations.

Example Scenario 1:

  * In Gringotts, picture a Human Relations* Cart resting stationary on a horizontal track. 
    * A force of 20 lb is applied to the side of the cart.
    * If drawn, the vector pictured should show an indication of magnitude, a point of application, and the direction along the line of action.
    * If the 20 lb force is not sufficient to move the cart, the cart has a balance of external forces acting on it and is said to be in _static equilibrium_.
    * Also represented within this example, the principle of _transmissibility_ states that a force acting on a body can be applied anywhere along the force’s line of action without changing its effect on the body. Thus, the force in this example would have an equal effect if applied on the other side of the cart in the same direction as application along the line of action.



* A note of caution: The Human Relations Departments at Gringotts is not what you think it is; be careful if you wish to speak to “HR.”

**Author's Note:**

> I do not own Harry Potter or anything not made up by myself.


End file.
